1. **State the problem:** Simplify the expression $$\frac{14a^{16}b^{13}}{-7a^{10}b^{11}}$$. 2. **Formula and rules:** When dividing powers with the same base, subtract the exponents: $$\frac{x^m}{x^n} = x^{m-n}$$. 3. **Simplify coefficients:** $$\frac{14}{-7} = \cancel{\frac{14}{-7}} = -2$$. 4. **Simplify powers of $a$:** $$\frac{a^{16}}{a^{10}} = a^{16-10} = a^6$$. 5. **Simplify powers of $b$:** $$\frac{b^{13}}{b^{11}} = b^{13-11} = b^2$$. 6. **Combine all parts:** $$-2a^6b^2$$. **Final answer:** $$\boxed{-2a^6b^2}$$